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In this article we focus on multiplier Hermitian-Einstein metrics introducedby Mabuchi which include K\"ahler-Einstein metrics, K\"ahler-Ricci solitons andMabuchi solitons as special cases. We also focus on KSM-manifolds, which areintroduced by the first author as toric bundles, to establish a criterion forthe existence of multiplier Hermitian-Einstein metrics in terms of KSM-data. Anexplicit example for a KSM-manifold admitting a family of multiplierHermitian-Einstein metrics is constructed by using a continuous path connectinga K\"ahler-Ricci soliton and a Mabuchi soliton.

Multiplier Hermitian-Einstein metrics on Fano manifolds of KSM-type